Year: 2026
Type: article
Abstract: We prove the existence of weak solutions and their continuous dependence on the data for a three-dimensional incompressible Navier-Stokes system subject to multivalued friction boundary conditions, within a Hilbert space framework. Under suitable assumptions, a fixed point argument yields the existence of a solution to the associated perturbed stationary problem. Using nonlinear semigroup theory, we then establish the existence of a mild solution to the non-stationary problem and prove a contraction principle. Finally, by combining the Crandall-Liggett implicit discretization scheme with a priori estimates for the approximating mild solutions, we obtain weak solutions that depend continuously on the initial data.
Authors: Simon ZONGO, BILA ADOLPHE KYELEM
Institution: University of Koudougou
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7169885983